Question

A binary star system consists of two stars of masses m1 and m2. The stars, which gravitationally attract each other, revolve around the center of mass of the system. The star with mass m1 has a centripetal acceleration of magnitude a1. Note that you do not need to understand universal gravitation to solve this problem.

Answer 1

Answer: $a_{2}=\frac{m_{1}}{m_{2}} a_{1}$

Explanation:

The rest of the question is below:

Find a2, the magnitude of the centripetal acceleration of the star with mass m2.

Assuming both stars are describing a uniform circular motion, their acceleration vector is directed towards the center of mass of the system (that's why it's called centripetal acceleration).  

Now, according to Newton's 2nd law, the force $F$ is directly proportional and in the same direction as the acceleration.

For $m_{1}$:

$F_{1}=m_{1}a_{1}$  

For $m_{2}$:

$F_{2}=m_{2}a_{2}$  

If the centripetal force is the same for both stars:

$F_{1}=F_{2}$  

$m_{1}a_{1}=m_{2}a_{2}$  

Isolating $a_{2}$:

$a_{2}=\frac{m_{1}}{m_{2}} a_{1}$